Class StringKernel

  • All Implemented Interfaces:
    java.io.Serializable, CapabilitiesHandler, OptionHandler, RevisionHandler, TechnicalInformationHandler

    public class StringKernel
    extends Kernel
    implements TechnicalInformationHandler
    Implementation of the subsequence kernel (SSK) as described in [1] and of the subsequence kernel with lambda pruning (SSK-LP) as described in [2].

    For more information, see

    Huma Lodhi, Craig Saunders, John Shawe-Taylor, Nello Cristianini, Christopher J. C. H. Watkins (2002). Text Classification using String Kernels. Journal of Machine Learning Research. 2:419-444.

    F. Kleedorfer, A. Seewald (2005). Implementation of a String Kernel for WEKA. Wien, Austria.

    BibTeX:

     @article{Lodhi2002,
        author = {Huma Lodhi and Craig Saunders and John Shawe-Taylor and Nello Cristianini and Christopher J. C. H. Watkins},
        journal = {Journal of Machine Learning Research},
        pages = {419-444},
        title = {Text Classification using String Kernels},
        volume = {2},
        year = {2002},
        HTTP = {http://www.jmlr.org/papers/v2/lodhi02a.html}
     }
     
     @techreport{Kleedorfer2005,
        address = {Wien, Austria},
        author = {F. Kleedorfer and A. Seewald},
        institution = {Oesterreichisches Forschungsinstitut fuer Artificial Intelligence},
        number = {TR-2005-13},
        title = {Implementation of a String Kernel for WEKA},
        year = {2005}
     }
     

    Valid options are:

     -D
      Enables debugging output (if available) to be printed.
      (default: off)
     -no-checks
      Turns off all checks - use with caution!
      (default: checks on)
     -P <0|1>
      The pruning method to use:
      0 = No pruning
      1 = Lambda pruning
      (default: 0)
     -C <num>
      The size of the cache (a prime number).
      (default: 250007)
     -IC <num>
      The size of the internal cache (a prime number).
      (default: 200003)
     -L <num>
      The lambda constant. Penalizes non-continuous subsequence
      matches. Must be in (0,1).
      (default: 0.5)
     -ssl <num>
      The length of the subsequence.
      (default: 3)
     -ssl-max <num>
      The maximum length of the subsequence.
      (default: 9)
     -N
      Use normalization.
      (default: no)

    Theory

    Overview

    The algorithm computes a measure of similarity between two texts based on the number and form of their common subsequences, which need not be contiguous. This method can be parametrized by specifying the subsequence length k, the penalty factor lambda, which penalizes non-contiguous matches, and optional 'lambda pruning', which takes maxLambdaExponent, m, as parameter. Lambda pruning causes very 'stretched' substring matches not to be counted, thus speeding up the computation. The functionality of SSK and SSK-LP is explained in the following using simple examples.

    Explanation & Examples

    for all of the following examples, we assume these parameter values:
     
    k=2
    lambda=0.5
    m=8 (for SSK-LP examples)
    

    SSK

    Example 1

    SSK(2,"ab","axb")=0.5^5 = 0,03125
    
    There is one subsequence of the length of 2 that both strings have in common, "ab". The result of SSK is computed by raising lambda to the power of L, where L is the length of the subsequence match in the one string plus the length of the subsequence match in the other, in our case:
       ab    axb
    L= 2  +   3 = 5
     
    hence, the kernel yields 0.5^5 = 0,03125

    Example 2

    SSK(2,"ab","abb")=0.5^5 + 0.5^4 = 0,09375
    
    Here, we also have one subsequence of the length of 2 that both strings have in common, "ab". The result of SSK is actually computed by summing over all values computed for each occurrence of a common subsequence match. In this example, there are two possible cases:
    ab    abb
    --    --  L=4
    --    - - L=5
     
    we have two matches, one of the length of 2+2=4, one of the length of 2+3=5, so we get the result 0.5^5 + 0.5^4 = 0,09375.

    SSK-LP

    Without lambda pruning, the string kernel finds *all* common subsequences of the given length, whereas with lambda pruning, common subsequence matches that are too much stretched in both strings are not taken into account. It is argued that the value yielded for such a common subsequence is too low (lambda ^(length[match_in_s] + length[match_in_t]) . Tests have shown that a tremendous speedup can be achieved using this technique while suffering from very little quality loss.
    Lambda pruning is parametrized by the maximum lambda exponent. It is a good idea to choose that value to be about 3 or 4 times the subsequence length as a rule of thumb. YMMV.

    Example 3

    Without lambda pruning, one common subsequence, "AB" would be found in the following two strings. (With k=2)
    SSK(2,"ab","axb")=0.5^14 = 0,00006103515625
    
    lambda pruning allows for the control of the match length. So, if m (the maximum lambda exponent) is e.g. 8, these two strings would yield a kernel value of 0:
    with lambda pruning:    SSK-LP(2,8,"AxxxxxxxxxB","AyB")= 0
    without lambda pruning: SSK(2,"AxxxxxxxxxB","AyB")= 0.5^14 = 0,00006103515625  
    
    This is because the exponent for lambda (=the length of the subsequence match) would be 14, which is > 8. In Contrast, the next result is > 0
    m=8
    SSK-LP(2,8,"AxxB","AyyB")=0.5^8 = 0,00390625
    
    because the lambda exponent would be 8, which is just accepted by lambda pruning.

    Normalization

    When the string kernel is used for its main purpose, as the kernel of a support vector machine, it is not normalized. The normalized kernel can be switched on by -F (feature space normalization) but is much slower. Like most unnormalized kernels, K(x,x) is not a fixed value, see the next example.

    Example 4

    SSK(2,"ab","ab")=0.5^4 = 0.0625
    SSK(2,"AxxxxxxxxxB","AxxxxxxxxxB") = 12.761724710464478
    
    SSK is evaluated twice, each time for two identical strings. A good measure of similarity would produce the same value in both cases, which should indicate the same level of similarity. The value of the normalized SSK would be 1.0 in both cases. So for the purpose of computing string similarity the normalized kernel should be used. For SVM the unnormalized kernel is usually sufficient.

    Complexity of SSK and SSK-LP

    The time complexity of this method (without lambda pruning and with an infinitely large cache) is
    O(k*|s|*|t|)
    Lambda Pruning has a complexity (without caching) of
    O(m*binom(m,k)^2*(|s|+n)*|t|)

    k...          subsequence length (ssl)
    s,t...        strings
    |s|...        length of string s
    binom(x,y)... binomial coefficient (x!/[(x-y)!y!])
    m...          maxLambdaExponent (ssl-max)
    
    Keep in mind that execution time can increase fast for long strings and big values for k, especially if you don't use lambda pruning. With lambda pruning, computation is usually so fast that switching on the cache leads to slower computation because of setup costs. Therefore caching is switched off for lambda pruning.

    For details and qualitative experiments about SSK, see [1]
    For details about lambda pruning and performance comparison of SSK and SSK-LP (SSK with lambda pruning), see [2] Note that the complexity estimation in [2] assumes no caching of intermediate results, which has been implemented in the meantime and greatly improves the speed of the SSK without lambda pruning.

    Notes for usage within Weka

    Only instances of the following form can be processed using string kernels:
    +----------+-------------+---------------+
    |attribute#|     0       |       1       |
    +----------+-------------+---------------+
    | content  | [text data] | [class label] |
    +----------------------------------------+
     ... or ...
    +----------+---------------+-------------+
    |attribute#|     0         |     1       |
    +----------+---------------+-------------+
    | content  | [class label] | [text data] |
    +----------------------------------------+
    
    Version:
    $Revision: 5518 $
    Author:
    Florian Kleedorfer (kleedorfer@austria.fm), Alexander K. Seewald (alex@seewald.at)
    See Also:
    Serialized Form
    • Field Detail

      • PRUNING_NONE

        public static final int PRUNING_NONE
        Pruning method: No Pruning
        See Also:
        Constant Field Values
      • PRUNING_LAMBDA

        public static final int PRUNING_LAMBDA
        Pruning method: Lambda See [2] for details.
        See Also:
        Constant Field Values
      • TAGS_PRUNING

        public static final Tag[] TAGS_PRUNING
        Pruning methods
    • Constructor Detail

      • StringKernel

        public StringKernel()
        default constructor
      • StringKernel

        public StringKernel​(Instances data,
                            int cacheSize,
                            int subsequenceLength,
                            double lambda,
                            boolean debug)
                     throws java.lang.Exception
        creates a new StringKernel object. Initializes the kernel cache and the 'lambda cache', i.e. the precalculated powers of lambda from lambda^2 to lambda^MAX_POWER_OF_LAMBDA
        Parameters:
        data - the dataset to use
        cacheSize - the size of the cache
        subsequenceLength - the subsequence length
        lambda - the lambda value
        debug - whether to output debug information
        Throws:
        java.lang.Exception - if something goes wrong
    • Method Detail

      • globalInfo

        public java.lang.String globalInfo()
        Returns a string describing the kernel
        Specified by:
        globalInfo in class Kernel
        Returns:
        a description suitable for displaying in the explorer/experimenter gui
      • getTechnicalInformation

        public TechnicalInformation getTechnicalInformation()
        Returns an instance of a TechnicalInformation object, containing detailed information about the technical background of this class, e.g., paper reference or book this class is based on.
        Specified by:
        getTechnicalInformation in interface TechnicalInformationHandler
        Returns:
        the technical information about this class
      • listOptions

        public java.util.Enumeration listOptions()
        Returns an enumeration describing the available options.
        Specified by:
        listOptions in interface OptionHandler
        Overrides:
        listOptions in class Kernel
        Returns:
        an enumeration of all the available options.
      • setOptions

        public void setOptions​(java.lang.String[] options)
                        throws java.lang.Exception
        Parses a given list of options.

        Valid options are:

         -D
          Enables debugging output (if available) to be printed.
          (default: off)
         -no-checks
          Turns off all checks - use with caution!
          (default: checks on)
         -P <0|1>
          The pruning method to use:
          0 = No pruning
          1 = Lambda pruning
          (default: 0)
         -C <num>
          The size of the cache (a prime number).
          (default: 250007)
         -IC <num>
          The size of the internal cache (a prime number).
          (default: 200003)
         -L <num>
          The lambda constant. Penalizes non-continuous subsequence
          matches. Must be in (0,1).
          (default: 0.5)
         -ssl <num>
          The length of the subsequence.
          (default: 3)
         -ssl-max <num>
          The maximum length of the subsequence.
          (default: 9)
         -N
          Use normalization.
          (default: no)
        Specified by:
        setOptions in interface OptionHandler
        Overrides:
        setOptions in class Kernel
        Parameters:
        options - the list of options as an array of strings
        Throws:
        java.lang.Exception - if an option is not supported
      • getOptions

        public java.lang.String[] getOptions()
        Gets the current settings of the Kernel.
        Specified by:
        getOptions in interface OptionHandler
        Overrides:
        getOptions in class Kernel
        Returns:
        an array of strings suitable for passing to setOptions
      • pruningMethodTipText

        public java.lang.String pruningMethodTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • setPruningMethod

        public void setPruningMethod​(SelectedTag value)
        Sets the method used to for pruning.
        Parameters:
        value - the pruning method to use.
      • getPruningMethod

        public SelectedTag getPruningMethod()
        Gets the method used for pruning.
        Returns:
        the pruning method to use.
      • setCacheSize

        public void setCacheSize​(int value)
        Sets the size of the cache to use (a prime number)
        Parameters:
        value - the size of the cache
      • getCacheSize

        public int getCacheSize()
        Gets the size of the cache
        Returns:
        the cache size
      • cacheSizeTipText

        public java.lang.String cacheSizeTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • setInternalCacheSize

        public void setInternalCacheSize​(int value)
        sets the size of the internal cache for intermediate results. Memory consumption is about 16x this amount in bytes. Only use when lambda pruning is switched off.
        Parameters:
        value - the size of the internal cache
      • getInternalCacheSize

        public int getInternalCacheSize()
        Gets the size of the internal cache
        Returns:
        the cache size
      • internalCacheSizeTipText

        public java.lang.String internalCacheSizeTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • setSubsequenceLength

        public void setSubsequenceLength​(int value)
        Sets the length of the subsequence.
        Parameters:
        value - the length
      • getSubsequenceLength

        public int getSubsequenceLength()
        Returns the length of the subsequence
        Returns:
        the length
      • subsequenceLengthTipText

        public java.lang.String subsequenceLengthTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • setMaxSubsequenceLength

        public void setMaxSubsequenceLength​(int value)
        Sets the maximum length of the subsequence.
        Parameters:
        value - the maximum length
      • getMaxSubsequenceLength

        public int getMaxSubsequenceLength()
        Returns the maximum length of the subsequence
        Returns:
        the maximum length
      • maxSubsequenceLengthTipText

        public java.lang.String maxSubsequenceLengthTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • setLambda

        public void setLambda​(double value)
        Sets the lambda constant used in the string kernel
        Parameters:
        value - the lambda value to use
      • getLambda

        public double getLambda()
        Gets the lambda constant used in the string kernel
        Returns:
        the current lambda constant
      • lambdaTipText

        public java.lang.String lambdaTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • setUseNormalization

        public void setUseNormalization​(boolean value)
        Sets whether to use normalization. Each time this value is changed, the kernel cache is cleared.
        Parameters:
        value - whether to use normalization
      • getUseNormalization

        public boolean getUseNormalization()
        Returns whether normalization is used.
        Returns:
        true if normalization is used
      • useNormalizationTipText

        public java.lang.String useNormalizationTipText()
        Returns the tip text for this property
        Returns:
        tip text for this property suitable for displaying in the explorer/experimenter gui
      • eval

        public double eval​(int id1,
                           int id2,
                           Instance inst1)
                    throws java.lang.Exception
        Computes the result of the kernel function for two instances. If id1 == -1, eval use inst1 instead of an instance in the dataset.
        Specified by:
        eval in class Kernel
        Parameters:
        id1 - the index of the first instance in the dataset
        id2 - the index of the second instance in the dataset
        inst1 - the instance corresponding to id1 (used if id1 == -1)
        Returns:
        the result of the kernel function
        Throws:
        java.lang.Exception - if something goes wrong
      • clean

        public void clean()
        Frees the memory used by the kernel. (Useful with kernels which use cache.) This function is called when the training is done. i.e. after that, eval will be called with id1 == -1.
        Specified by:
        clean in class Kernel
      • numEvals

        public int numEvals()
        Returns the number of kernel evaluation performed.
        Specified by:
        numEvals in class Kernel
        Returns:
        the number of kernel evaluation performed.
      • numCacheHits

        public int numCacheHits()
        Returns the number of dot product cache hits.
        Specified by:
        numCacheHits in class Kernel
        Returns:
        the number of dot product cache hits, or -1 if not supported by this kernel.
      • normalizedKernel

        public double normalizedKernel​(char[] s,
                                       char[] t)
        evaluates the normalized kernel between s and t. See [1] for details about the normalized SSK.
        Parameters:
        s - first input string
        t - second input string
        Returns:
        a double indicating their distance, or similarity
      • unnormalizedKernel

        public double unnormalizedKernel​(char[] s,
                                         char[] t)
        evaluates the unnormalized kernel between s and t. See [1] for details about the unnormalized SSK.
        Parameters:
        s - first input string
        t - second input string
        Returns:
        a double indicating their distance, or similarity
      • buildKernel

        public void buildKernel​(Instances data)
                         throws java.lang.Exception
        builds the kernel with the given data.
        Overrides:
        buildKernel in class Kernel
        Parameters:
        data - the data to base the kernel on
        Throws:
        java.lang.Exception - if something goes wrong, e.g., the data does not consist of one string attribute and the class